A Minimum Threshold for Wind Profiler Signal-to-Noise Ratios

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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY

JULY 2012

A Minimum Threshold for Wind Profiler Signal-to-Noise Ratios ANTHONY C. RIDDLE* CIRES, University of Colorado, Boulder, Colorado

LESLIE M. HARTTEN, DAVID A. CARTER, PAUL E. JOHNSTON, AND CHRISTOPHER R. WILLIAMS CIRES, University of Colorado, and NOAA/Earth System Research Laboratory/Physical Sciences Division, Boulder, Colorado (Manuscript received 30 September 2011, in final form 29 December 2011) ABSTRACT One limiting factor in atmospheric radar observations is the inability to distinguish the often weak atmospheric signals from fluctuations of the noise. This study presents a minimum threshold of usability, SNRmin, for signal-to-noise ratios obtained from wind profiling radars. The basic form arises from theoretical considerations of radar noise; the final form includes empirical modifications based on radar observations. While SNRmin was originally developed using data from the 50-MHz profiler at Poker Flat, Alaska, it works well with data collected from a wide range of locations, frequencies, and parameter settings. It provides an objective criterion to accept or reject individual spectra, can be quickly applied to a large quantity of data, and has a false-alarm rate of approximately 0.1%. While this threshold’s form depends on the methods used to calculate SNR and spectral moments, variations of the threshold could be developed for use with data processed by other methods.

1. Introduction Wind profilers are Doppler radars with antenna beams pointing in fixed vertical and near-vertical directions. They use lower frequencies (30–2900 MHz) than scanning weather radars (2.7–12.0 GHz) to detect Bragg scatter from inhomogeneities in the refractive index (Gage and Balsley 1978), which are generated by turbulent perturbations of pressure, temperature, and humidity, and then advected by the wind. Wind profilers are also sensitive to Rayleigh scattering from falling hydrometeors, enabling them to observe both vertical air motion and precipitation motion when the radar beam is pointed vertically (Fukao et al. 1985; Wakasugi et al. 1986; Williams and Gage 2009). The first clear-air wind profiles were made in the stratosphere and mesosphere with a 50-MHz radar located at Jicamarca, Peru (Woodman and Guillen 1974). Wind profilers are routinely deployed in field experiments

* Deceased.

Corresponding author address: Leslie M. Hartten, CIRES, University of Colorado, 216 UCB, Boulder CO 80309-0216. E-mail: [email protected]

and there are several operational profiler networks, for example, the National Oceanic and Atmospheric Administration (NOAA)’s Profiler Network (NPN) in the United States (Weber and Wuertz 1990), the European Cooperation in Science and Technology (COST) Wind Initiative for a Network Demonstration in Europe (CWINDE) in Europe (Nash and Oakley 2001), and the Wind Profiler Network and Data Acquisition System (WINDAS) in Japan (Ishihara et al. 2006). Backscatter from clear-air turbulence is a weak scattering mechanism, so the signal received from the atmosphere is very small. Detection of small signals is a classic radar problem (cf. DiFranco and Rubin 1980), although the wind-profiling radar case is unique, in that both coherent and incoherent averages are utilized. The basic idea is to establish a criterion that specifies that an echo, or signal, has been detected. One way to do this is to set a signal-to-noise ratio (SNR) threshold. SNR values larger than this threshold are declared to be signals, while values below it are determined to not be signals. Using a threshold based on SNR instead of signal alone is especially advantageous at lower frequencies (e.g., 50 MHz), where cosmic noise can vary 6–10 dB during a day. Two potential errors are associated with setting a threshold. A false-alarm error comes from setting the

DOI: 10.1175/JTECH-D-11-00173.1 Ó 2012 American Meteorological Society

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threshold too low, so that detection is declared when there is no signal present. If the threshold is set too high, then a signal that is present is not detected and a miss error occurs. Achieving the proper balance between the two errors is situation dependent. In meteorological applications, the costs of including bad data are generally greater than the costs of omitting good data. We present one tool for determining echo existence from any single-point measurement, a minimum threshold of usability for SNR. The threshold was developed empirically in the 1980s using fundamental radar properties (Riddle et al. 1989; Riddle 1990, 1992) and data from a 50-MHz profiler deployed at Poker Flat, Alaska. While widely used over the last two decades (e.g., Chang et al. 1997; Vaisala Oyj 2004; W. O. J. Brown 2010, personal communication), the formula has not been published in peer-reviewed literature. This threshold can be used with data collected by profilers using averaged power spectra and spectral moments as specified by Woodman (1985), Barth et al. (1994), and Carter et al. (1995). These include the NOAA Profiler Network’s 35 radars (http://www.profiler.noaa.gov/npn/), more than 250 Vaisala and Radian systems worldwide (J. W. Neuschaefer 2011, personal communication), and most research systems deployed by NOAA’s Earth System Research Laboratory and its predecessors. As profiler data becomes more widely available to researchers who do not work closely with profiler specialists, it seems past time to document exactly what this threshold applies to and what its affects are.

2. Our profiler operations and threshold development Most wind profilers follow the same basic signalprocessing principles, although the exact implementation varies. The radar is set to dwell for a certain length of time in each antenna direction. During each dwell, 105 to more than 106 radio pulses are transmitted, with backscattered returns received from multiple ranges. The time between pulses is set by the interpulse period (IPP). The analog signal received from the antenna is amplified, filtered, and converted to digital samples representing the vector voltages received at particular times. Samples from each range are collected for a specified number of IPPs and processed using a sequence of signal-processing techniques designed to extract the atmospheric echoes from the noise. The samples from all ranges are processed using the same methods. First, consecutive voltage samples are averaged in a process called coherent integration. The result is divided into NSpec segments, where NSpec is the number of spectra averaged together before noise power and spectral

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FIG. 1. One averaged power spectrum (Npts 5 256; NSpec 5 16), showing spectral power as a function of radial velocity, from the Wallops Island 2835-MHz profiler (0000:01 UTC 29 Jul 2006). Light gray shading extends upward to hni, Pn equals the entire light gray area, and Ps equals the area shaded with dark gray. Dashed gray line indicates hni 1 sn, the standard deviation of the noise. Value of the first spectral moment, radial velocity, is indicated by a vertical line and the size of twice the square root of the second moment, spectral width, by a horizontal line.

moments are calculated; each NPts long, where NPts is the number of points in the specta; and a von Hann window is applied to each. Next, a Fourier transform is applied to each of the windowed segments and the output is squared, yielding NSpec velocity power spectra. Finally, these power spectra are averaged together in a process called incoherent averaging. From the resulting averaged power spectrum (Fig. 1), the noise power and spectral moments are calculated: signal power (zeroth moment), Doppler velocity (first moment), and spectral width (from the second moment). SNR is computed from the noise and signal powers. Our method of analyzing each averaged power spectrum can be divided into four steps. First, the mean noise density hni is determined using the Hildebrand–Sekhon method (Hildebrand and Sekhon 1974) as modified for an averaged power spectrum. This establishes the noise power as Pn 5 hni 3 NPts. Second, the largest peak of the spectrum is identified. Third, the signal is identified as those points near this peak that are above hni. The sum of these points, with hni removed, is the signal power Ps. Finally, the radial velocity and spectral width of the identified signal are calculated. This method always computes noise, Ps, radial velocity, and spectral width for each averaged power spectrum, even if there is no signal present (i.e., if the return comprised only noise). The problem is how to decide when a signal is present, based only on the SNR of an averaged power spectrum. The standard deviation of the noise density, sn, relative to the peak signal is important in this detection, but since

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Ps is an integrated value, the ratio of the signal peak to sn is an insufficient criterion. However, fundamental properties of random variables suggest a basic form. The variance of an average of independent samples of a random variable equals the variance of the individual observations divided by the number N of measurements in the average, so thepstandard deviation about the mean ffiffiffiffi will be related to 1/ N . The FFT used to create the velocity power spectrum has the statistics of an average of NPts, so the FFT values can be considered as averages in voltage, which are then converted to power by squaring, so the standard deviation of Pn in a power spectrum is related to 1/NPts. Likewise, the standard deviation of hniffi pffiffiffiffiffiffiffiffiffiffiffiffiffi in an average of power spectra is related to 1/ NSpec. This yields a detection criterion with the basic form of SNRmin

! constant pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 10 log NPts NSpec

(1)

with SNRmin in decibels. Noise statistics are well understood; the noise voltages at the output of the receiver are white noise with a zero mean Gaussian distribution. Therefore, the power in an averaged power spectrum of pure noise follows a chi-square distribution with 2NSpec degrees of freedom (Petitdidier et al. 1997). As NSpec increases, s2n decreases and the distribution of the noise becomes closer to Gaussian. However, for small NSpec the chi-square distribution is asymmetrical with a long tail that will increase the false-alarm rate associated with (1). Tests using some large subset of the data collected at Poker Flat1 from 1979 to 1987 led to the empirical modification of the threshold, yielding 3 2 170 1/2 25 NSpec 2 2:3125 1 6 NPts 7 7. SNRmin 5 10 log6 5 4 NPts 3 NSpec

(2)

The square root term is required to be .0.2 (Riddle 1990), although this requirement is not always reported (e.g., Riddle et al. 1989; Vaisala Oyj 2004). A key point of this threshold is that it applies to an individual averaged power spectrum; it makes no assumptions about measurements made close in space or time to the spectrum that is being evaluated. Thus, it can serve as an objective determination of a spectrum’s usability. This was critical with data from the 50-MHz Poker Flat profiler, which operated in atmospheric conditions

1 Details of the Poker Flat operating parameters can be found in Table 1.

FIG. 2. Averaged spectra (NPts 5 128) from (a) the 5.18-km range gate of the Tarawa 915-MHz profiler, 2049:17 UTC 1 Apr 1998; (b) the 10.40-km range gate of the Christmas Island 50-MHz profiler, 2244:38 UTC 1 Apr 1999; and (c) the 4.64-km range gate of the Christmas Island 915-MHz profiler, 0650:00 UTC 1 Apr 1999. See Table 1 for more details about each profiler. Spectral power of each spectrum has been normalized so that the noise density equals 1, and the x axis is presented as spectral points instead of radial velocity. Noise power is shaded gray, and gray dashed lines are placed one standard deviation above the mean noise level. Dark vertical line on each spectrum indicates the location of the spectral peak, while dark horizontal line indicates the spectral width. SNR and SNRmin for each spectrum are shown in the top-left corner of each panel. Based on SNRmin, the spectrum in (c) would be rejected as not having usable signal.

that often yielded echoes isolated in time and space. It remains useful in other settings; it can be easily automated and applied to large amounts of data, and it mitigates against human errors when data are evaluated manually. Figure 2 shows averaged power spectra taken from three different radars, arranged so that SNR

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as they often are in display software, our eyes are likely to pick out a feature such as the indicated peak in Fig. 2c because its location is similar to peaks in spectra displayed near it, even though that spectrum’s SNR is quite low. Values of SNRmin for the range of NPts and NSpec typical in wind profiling are presented in Fig. 3. The gray curves, calculated without the 170/NPts term, show that this term’s effects are most important when NPts and NSpec are small.

3. Comparisons with data FIG. 3. Values of SNRmin as a function of NSpec for various values of NPts. For NPts # 256, SNRmin is calculated using NSpec $ 2; for larger NPts, SNRmin cannot be calculated at NSpec 5 2 because of the constraints on Eq. (2) discussed in the text. Large diamonds indicate parameter sets listed in Table 1; all four values with NPts 5 64 are from the Poker Flat 50-MHz system. Gray curves show what SNRmin would be if the 170/NPts term were omitted from Eq. (2).

approximately equals SNRmin 13 dB (Fig. 2a), SNRmin (Fig. 2b, even though the peak is higher than in Fig. 2a), and SNRmin 23dB (Fig. 2c, which would lead to the rejection of the peak). When spectra are arranged this way,

Before deciding to use a threshold, it is important to understand the potential errors associated with it. To determine the false-alarm rate for SNRmin, we operated a radar system in the laboratory with a noise diode on the input to the receiver, setting NPts 5 128 and NSpec 5 32. This simulates a radar running with the transmitter turned off and gives us data that we know have no signal present. Of 2 704 158 independent observations, 3300 were above SNRmin, a false-alarm rate of 0.122%. It is much harder to establish the miss rate associated with a threshold. The fact that the noise has a white

TABLE 1. Key specifications and operating parameters for profilers discussed in this paper, together with the corresponding Riddle threshold, SNRmin. ‘‘Year’’ refers to the year from which the presented data are drawn; specific days, when applicable, are given in the text or figure. If pulse coding was used, the type appears in parentheses beside the PW. Frequency (MHz)

Location

Christmas Island (1999), Republic of Kiribati Christmas Island (1999), Republic of Kiribati Poker Flat (1984), Alaska Poker Flat (1979), Alaska Poker Flat (1979), Alaska Poker Flat (1984), Alaska Swedish Icebreaker Oden (2008) Christmas Island (1999), Republic of Kiribati Estacioń Obispo (2004), Sinaloa, Mexico Moody (2005), Texas Moody (2005), Texas Tarawa (1998), Republic of Kiribati Tarawa (2002), Republic of Kiribati Tarawa (2002), Republic of Kiribati Wallops Island (2006), Virginia

28N, 1578W

50

4 oblique

4

128

1 ms

6.7 ms

210.72

28N, 1578W

50

1 vertical

2

256

1 ms

6.7 ms

215.38

658N, 1478W 658N, 1478W 658N, 1478W 658N, 1478W 878N, 38W

50 50 50 50 449

2 oblique, 1 vertical 2 oblique, 1 vertical 2 oblique, 1 vertical 2 oblique, 1 vertical 2 oblique, 1 vertical

9 20 64 99 16

64 64 64 64 256

28N, 1578W

915

4 oblique, 1 vertical

44

128

90 ms

3.3 ms

215.36

148N, 918W

915


100

128

38 ms

0.4 ms

217.11

318N, 978W 318N, 978W 18N, 1738E

915 915 915

4 oblique, 1 vertical 1 vertical* 2 oblique, 1 vertical

32 40 51

128 2048 128

43 ms 200 ms 127 ms

0.417 ms (4 bit) 0.417 ms 3.3 ms

214.69 227.27 215.67

18N, 1738E

915


35

256

249 ms

2.6 ms (4 bit)

217.93

18N, 1738E

915


31

256

58 ms

0.6 ms (4 bit)

217.68

758N, 388W

2835

1 vertical**

16

256

124 ms

0.208 ms

216.36

* This was a radio acoustic sounding system (RASS) mode. ** This was a precipitation mode.

Beams

NSpec

NPts

IPP

850 850 850 850 134

ms ms ms ms ms

PW (code)

SNRmin (dB)

Site name (year)

16 ms 16 ms 16 ms 16 ms 1.417 ms (8 bit)

28.77 210.55 213.10 214.05 216.36

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FIG. 4. Scatterplots of SNR vs radial velocity collected by (a) a 449-MHz profiler aboard the Swedish Icebreaker Oden on 22 Aug 2008, (b) a 915-MHz profiler at Moody on 13 Nov 2005, (c) a 2835-MHz profiler at Wallops Island on 29 Jul 2006, (d) a 915-MHz profiler at Tarawa on 13 Aug 2002, and (d) a 50-MHz profiler at Christmas Island on 1 Apr 1999. See Table 1 for more details about each profiler. Only data from the first 20 min of each hour are included in (c). In all cases, data with SNR above 0 dB are not shown. Total number of independent points available, including those with SNR above 0 dB, is (a) 66 880, (b) 220 880, (c) 398 000, (d) 53 280, and (e) 31 356. Thick vertical line in each plot indicates the SNRmin calculated from that profiler’s parameters.

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frequency distribution means that the velocities determined from noise will be uniformly distributed across the velocity range measured by the profiler. Velocities from actual targets tend not to be random, but rather cluster in one or more small ranges of velocity. Examining a large number of SNRs from any given profiler reveals many very low SNRs whose associated radial velocities are distributed fairly evenly across all possible values, indicating that the bulk of them are noise rather than atmospheric or precipitation echoes. We have confirmed this using data from several different profilers, chosen to maximize the range of operating parameters and conditions. These systems were deployed from the tropics to the Arctic at a mix of oceanic and continental locations, and operated at four different frequencies. Key specifications and operating parameters are shown in Table 1. For each profiler we chose one random day for analysis; this yielded tens or hundreds of thousands of SNRs. If a profiler operated in multiple modes, then each was analyzed separately. Data from Poker Flat were not used in this analysis. Examples from five profilers are shown in Fig. 4, with SNR plotted versus radial velocity. To highlight the noise region, only SNRs below 0 dB are shown, and because of the volume of data involved, only values from the first 20 min of each hour at Wallops Island were plotted. At the lowest SNRs, the full range of possible radial velocities are present, while in the highest 5–15 dB of plotted SNRs, the velocities are tightly clustered. Two or three signal clusters are apparent in systems with multiple beams or with both clear-air and precipitation echoes (Fig. 4c). While it is difficult to measure the threshold’s miss rate from these data, it is clear that reducing the threshold, which might decrease the miss rate, would also quickly increase the false-alarm rate.

4. Final remarks We have presented here a minimum threshold of usability, SNRmin, for SNRs obtained from wind-profiling radars. The threshold’s basic form arises from theoretical considerations of radar noise; the final form is an empirical modification. The threshold can be applied to each individual power spectrum to determine if there is a signal present. Its dependence on basic profiler parameters makes it easy to use with a large volume of data. The threshold compares well with profiler data collected at a wide range of locations, frequencies, and parameter settings. It provides an objective criterion to accept the moments from individual estimates of the backscattered power spectra as not being noise. It works well at small values of NSpec when the noise power probability frequency distribution has a long

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positive tail and has a false-alarm rate of approximately 0.1%. If an experiment can tolerate a higher error rate, then it is easy to adjust SNRmin down. Conversely, if this error rate is too high, then the threshold can be increased. As described in section 2, the threshold rests on assumptions about how SNR and spectral moments are calculated: that the received data consist of one signal plus noise, and that the signal is the largest peak in the spectrum. These assumptions were good for the Poker Flat 50-MHz system and remain good for many profilers. In situations where these assumptions are violated, the threshold may need modification. Sometimes there are multiple signals in the data requiring different methods to extract the atmospheric data from the averaged power spectra, which can affect the statistics of the signal and noise. Other methods of determining the signal power also require a modification to the threshold. The threshold remains useful for many current datasets, providing an objective criterion to help evaluate the usability of data. Furthermore, there is no particular reason why variations of SNRmin could not be developed for these other situations. Acknowledgments. Dr. Anthony C. Riddle received his Ph.D. in electrical engineering from Stanford University, and spent much of his career doing radio astronomy and dealing with both signals in noise and noise as a signal. He died in December 2004, seven years after ‘‘retiring’’ from CIRES. We coauthors, who worked with him for many years at NOAA’s Aeronomy Laboratory and still make use of his computer code, datasets, and scientific results, miss Tony’s energetic and rigorous approach to data analysis and quality control, his creativity, and most of all his ready and good-humored conversation. This research was supported by grants from NOAA’s Office of Global Programs to NOAA’s Earth System Research Laboratory.

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